Results 1 to 10 of about 119,691 (156)

Similarity and Coincidence Isometries for Modules [PDF]

, 2010
The groups of (linear) similarity and coincidence isometries of certain modules in d-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered.
Adkins, Baake, Baake, Baake, Baake, Borevich, Pleasants, Scott, Svenja Glied   +8 more
core   +1 more source

Early contributions of crystallography to the atomic theory of matter

Acta Crystallographica Section A: Foundations and Advances, 2018
After briefly presenting early hypotheses on the submicroscopic origin of symmetry and polyhedral morphology in the crystals, the structural model proposed by Hauy in 1784, based on the periodic repetition of integrant molecules made up of simple ...
G. Ferraris
semanticscholar   +1 more source

Countable groups are mapping class groups of hyperbolic 3-manifolds

, 2005
We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.Comment: 15 pages, 6 ...
Frigerio, Roberto, Martelli, Bruno
core   +2 more sources

Graph theoretic methods for the analysis of structural relationships in biological macromolecules [PDF]

, 2005
Subgraph isomorphism and maximum common subgraph isomorphism algorithms from graph theory provide an effective and an efficient way of identifying structural relationships between biological macromolecules.
Altschul, Artymiuk, Artymiuk, Artymiuk, Artymiuk, Artymiuk, Barnard, Baxevanis, Benning, Berman, Bernstein, Brint, Brint, Bron, Bruno, Bryant, Crandell, Dean, Diestel, Doubet, Fan, Feizi, Figueras, Flores, Gardiner, Gati, Good, Gray, Groves, Gruer, Gund, Hagadone, Harrison, Holden, Hutchinson, Jasanoff, Johnson, Kanna, Klausner, Kleywegt, Koch, Kraulis, Lengauer, Lesk, Martin, Martin, McGregor, Messmer, Mitchell, Ollis, Pickering, Ray, Raymond, Read, Salton, Samudrala, Sayle, Simon, Srere, Sussenguth, Tesmer, Tinoco, Trinajstic, Tsukada, Ullmann, van Rijsbergen, Willett, Willett, Willett, Willett, Williams, Wilson, Zhang   +72 more
core   +3 more sources

Initiating Heavy-atom Based Phasing by Multi-Dimensional Molecular Replacement

, 2014
To obtain an electron-density map from a macromolecular crystal the phase-problem needs to be solved, which often involves the use of heavy-atom derivative crystals and concomitantly the determination of the heavy atom substructure.
Gourdon, Pontus, Karlsen, Jesper Lykkegaard, Liu, Xiangyu, Nissen, Poul, Pedersen, Bjørn Panyella   +4 more
core   +1 more source

Review

, 2020
The chalcogen elements oxygen, sulfur, and selenium are essential constituents of side chain functions of natural amino acids. Conversely, no structural and biological function has been discovered so far for the heavier and more metallic tellurium ...
Agh R, Arai K, Baskakov IV, Creighton TE, Dittmer K, Du Vigneaud V, Janeček J, Metanis N, Musiol HJ, Muttenthaler M, Nygard B, O'Donnell ME, Welch M, Yang F   +13 more
core   +1 more source

Crystallography in Spaces E 2 , E 3 , E 4 , E 5 … Study of Three Crystal Families of Space E 5

, 2017
In two previous papers, we explained the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes and we describe some crystal families.
R. Veysseyre, D. Weigel, H. Veysseyre
semanticscholar   +1 more source

Aligned SICs and embedded tight frames in even dimensions

, 2019
Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one in dimension $d$ and another in dimension $d(d-2)$, manifesting a well-founded conjecture about a number-theoretical connection between the SICs. In this paper, we prove that if
Andersson, Ole, Dumitru, Irina
core   +1 more source

How model sets can be determined by their two-point and three-point correlations

, 2009
We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations.
A. Hof, C. Radin, D. Mermin, D.J. Daley, F.J. Grünbaum, J. Bellissard, J. Fell, J.-B. Gouéré, J.L. Kelly, J.Y. Lee, L. Patterson, M. Baake, M. Baake, M. Reed, M. Schlottmann, N. Bourbaki, P. Jaming, R.V. Moody, R.V. Moody, R.V. Moody, Robert V. Moody, U. Grimm, U. Grimm, X. Deng, Xinghua Deng   +24 more
core   +2 more sources

Categories without structures [PDF]

, 2009
The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics.
Rodin, Andrei
core   +5 more sources